The Complete Heirlooms Guide (WotLK & Cataclysm)

*** What are Heirlooms? ***Heirlooms are items that Bind to your Account and scale with the level of the character that wears them. They can be sent via mail to different characters on the same account, and worn by them. Some heirloom items provide XP bonuses upon equip.

*** Cataclysm Expansion ***- Via Guild Achievements (more on this after the Wrath of the Lich King info - scroll down!)

*** How can Justice Points/Seals be obtained? ****** Wrath of the Lich King Expansion ***As an important note, absolutely ALL Wrath of the Lich King Heirlooms will stop scaling and giving bonuses after you've reached level 80. If you want bonuses for the Cataclysm expansion, you must purchase Cataclysm specific Heirlooms, which are described after the Wrath of the Lich King information!

There are different ways to obtain the currencies required within the game.
All the tips and tricks are down below!

Justice Points:

Since the introduction of the Random Dungeon Finder system and the introduction of Cataclysm, you will get Justice Points for every random dungeon completed, in addition to the ones that drop from bosses.

In addition to all these bonuses, every week there's a new raid weekly quest, which can be completed on every difficulty of every size raid, that has you kill someone. The rewards for that raid quest are Justice Points. The quest is started every week byArchmage Lan'dalock - NPC - World of Warcraft

Champion's Seals can be obtained by participating in the Argent Tournament.

Once you arrive on-site (northern Icecrown), you will be given some quests to complete to get you started in the Tournament. Once you've done the basics, you can choose to become a Valiant (and later on a Champion) of one of faction's races. The number of days it takes to become a Champion of a race is 5, totaling 25 days to be a Champion of your faction. If you have exalted reputation with the races you become a champion with, you will get the ability to buy those races' mounts/pets/items, plus a custom Title. It is recommended to do all the dailies obtainable from the Tournament Grounds, to maximize your Champion's Seal income.

Once you're a champion of all 5 races of your faction, new daily quests unlock. When you've completed all steps and acquired all the Chapion statuses, you will get roughly 10 Champion's Seals per day by doing the dailies provided each day.

Since the quest list is so long, please take a peek at the item's tooltip page to see all quests that reward Champion's Seals, sorted by faction.

*** Armor ***Shoulder pieces (+10% XP bonus) are available in PvE or PvP versions.
PvE versions can be bought from Dalaran or Icecrown. PvP versions can be bought from Wintergrasp, when your faction controls the fortress.

*** Enchanting your Heirlooms ***Heirloom items are treated as iLvl 1 items, so you cannot enchant them with some Vanilla, Burning Crusade or older enchants.

This is not entirely accurate. Glyphs/arcanum and inscriptions can be applied to heirloom helms and shoulders, respectively, despite their failing the iLvl requirements; they simply will not offer the benefit of the enhancement until the user reaches the appropriate level.

You didn't list out the Cloak Enchants and forgot to mention Blood Draining and Blade Ward

Also:
'Heirloom items are treated as iLvl 1 items, so you cannot enchant them with some Vanilla, Burning Crusade or olderenchants.'
Don't you mean 'newer'? And I honestly can't think of even one Vanilla enchant you cannot use.

I am sorry, I haven't tested the arcanums on Heirlooms to be able to say if they work or not. Also, I have been inactive in World of Warcraft for quite some time. I am thankful that people point out the mistakes that I've made, and I will correct them when I have the time. Thank you.

Those enchants are wrath enchants. And you can only use pre-BC enchants on BoA.

I haven't tried it with BC/WotLK enchants per se, but will point out that helm and shoulder enchants from BC & WotLK can be applied to heirlooms (they just don't offer the bonuses till the character meets the level requirement).